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   <div id="projectname">gbmath
   &#160;<span id="projectnumber">v0.051</span>
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   <div id="projectbrief">c++ math library</div>
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<div class="title">scalar.h</div>  </div>
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<a href="scalar_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;﻿</div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#ifndef __GBMATH_H__</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor"></span><span class="preprocessor">    #error  DO NOT INCLUDE THIS FILE. USE:   #include &lt;gbmath/_gbmath.h&gt;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span>gbmath</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;{</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;         </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;         </div>
<div class="line"><a name="l00019"></a><span class="lineno"><a class="code" href="namespacegbmath.html#aefe79f6a1175131aecf3149f0fec6d49">   19</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespacegbmath.html#aefe79f6a1175131aecf3149f0fec6d49">compare</a>(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b, <span class="keywordtype">float</span> epsilon)</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    {</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <span class="keywordflow">return</span> fabs(a - b) &lt; epsilon;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    }</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div>
<div class="line"><a name="l00026"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a30da8e56355a72f9d2565cbf89179153">   26</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespacegbmath.html#a30da8e56355a72f9d2565cbf89179153" title="Check the value the correct value. ">check</a>(<span class="keywordtype">float</span> f)</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    {</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;           <span class="keywordflow">if</span>( f == 0.0f ) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;           <span class="keywordflow">if</span>(f &lt; 0.0f)    f = -f;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;           <span class="keywordflow">if</span>( (f &lt;= FLT_MAX) &amp;&amp; (f &gt;= FLT_MIN) ) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;           <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    }</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div>
<div class="line"><a name="l00036"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ac312471790333df7fed15517524443b9">   36</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespacegbmath.html#a30da8e56355a72f9d2565cbf89179153" title="Check the value the correct value. ">check</a>(<span class="keywordtype">double</span> d)</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    {</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;       <span class="keywordflow">if</span>( d == 0.0 ) </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;           <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;       <span class="keywordflow">if</span>(d &lt; 0.0) </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;           d = -d;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;       <span class="keywordflow">if</span>( (d &lt;= DBL_MAX) &amp;&amp; (d &gt;= DBL_MIN) ) </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;           <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;       <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    }</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;</div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="code" href="namespacegbmath.html#af7ceb382df8a74edbe983b1745229cce">   52</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#af7ceb382df8a74edbe983b1745229cce" title="x*x ">sqr</a>(<span class="keywordtype">float</span> x) </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    { </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <span class="keywordflow">return</span> x*x; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    }</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a6770b1369e60e627d9e86b8ec68188e1">   57</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#a6770b1369e60e627d9e86b8ec68188e1">abs</a>(<span class="keywordtype">float</span> val)</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    {</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keywordflow">if</span>(val&lt;0.0f)</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        {</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;            <span class="keywordflow">return</span> -val;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        }</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordflow">return</span> val;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    }</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a30742374d53e9b267e9efa8dc80a0a91">   70</a></span>&#160;    <span class="keyword">inline</span> T <a class="code" href="namespacegbmath.html#a30742374d53e9b267e9efa8dc80a0a91" title="Calculate the linear interpolation. ">lerp</a>( <span class="keywordtype">float</span> alpha, <span class="keyword">const</span> T&amp; v0, <span class="keyword">const</span> T&amp; v1 ) <span class="keywordflow">throw</span>()</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    {</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="keywordflow">return</span>( (T)(v0 + alpha * ( v1 - v0 )) );</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    }</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;</div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a5292b82144444629c81be0728104e8ab">   76</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#a5292b82144444629c81be0728104e8ab" title="bilinear interpolation ">bilerp</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> a, <span class="keyword">const</span> <span class="keywordtype">float</span> b, <span class="keyword">const</span> <span class="keywordtype">float</span> c, <span class="keyword">const</span> <span class="keywordtype">float</span> d, <span class="keywordtype">float</span> u, <span class="keywordtype">float</span> v)</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    {</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">return</span> a * ((1.0f - u) * (1.0f - v)) + b * (u * (1.0f - v)) + c * (v * (1.0f - u)) + d * (u * v);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    }</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a30b7c446b59840332a8e001a80316bc5">   83</a></span>&#160;    <span class="keyword">inline</span> T <a class="code" href="namespacegbmath.html#a30b7c446b59840332a8e001a80316bc5" title="reduction in the range between ">clamp</a>( <span class="keyword">const</span> T&amp; v, <span class="keyword">const</span> T&amp; l, <span class="keyword">const</span> T&amp; u ) <span class="keywordflow">throw</span>()</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    {</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <span class="keywordflow">return</span> min(u, max(l,v));</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a07b847494d285fb1532c8718a6cb2fbd">   91</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespacegbmath.html#a07b847494d285fb1532c8718a6cb2fbd" title="fill the buffer dest value val number num. ">fill</a>( T * dest, <span class="keyword">const</span> T val, <span class="keyword">const</span> <span class="keywordtype">int</span> num ) <span class="keywordflow">throw</span>()</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    {</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num; i++)</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;            dest[i] = val;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        }</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    }</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ae98efd1a452855c4e8c7e8ef08bab2a1">  105</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span>  <a class="code" href="namespacegbmath.html#ae98efd1a452855c4e8c7e8ef08bab2a1" title="Returns the sign of   x&gt;0 : 1   x=0 : 0   x&lt;0 : -1. ">sign</a> (<span class="keyword">const</span> <span class="keywordtype">float</span> val)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordflow">if</span>(val==0.0f)</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;          <span class="keywordflow">return</span> 0.0f;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keywordflow">if</span>(val&gt;0.0f)</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;          <span class="keywordflow">return</span> 1.0f;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="keywordflow">return</span> -1.0f;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    </div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a273bd63fdf09037f17ea3ef69c037528">  122</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="namespacegbmath.html#a273bd63fdf09037f17ea3ef69c037528" title="Returns the sign of   x&gt;0 : 1   x=0 : 0   x&lt;0 : -1. ">sign2</a>(<span class="keywordtype">float</span> x)</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    {</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        <span class="keywordflow">return</span>  (x&gt;0)-(x&lt;0);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    }</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;</div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ab28d0d43c10be205a0fc2aa114241330">  131</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespacegbmath.html#ab28d0d43c10be205a0fc2aa114241330" title="All angles are in radians. rho = distance from origin O to point P (i.e., length of OP) phi = angle b...">cartesianToSpherical</a>(<span class="keywordtype">float</span> x, <span class="keywordtype">float</span> y, <span class="keywordtype">float</span> z, <span class="keywordtype">float</span> &amp;rho, <span class="keywordtype">float</span> &amp;phi, <span class="keywordtype">float</span> &amp;theta )</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        rho = sqrtf((x * x) + (y * y) + (z * z));</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        phi = asinf(y / rho);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        theta = atan2f(z, x);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    }</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    </div>
<div class="line"><a name="l00142"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a343f1f71e8a00aa022050fd353b0f84a">  142</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespacegbmath.html#a343f1f71e8a00aa022050fd353b0f84a" title="All angles are in radians. rho = distance from origin O to point P (i.e., length of OP) phi = angle b...">sphericalToCartesian</a>(<span class="keywordtype">float</span> rho, <span class="keywordtype">float</span> phi, <span class="keywordtype">float</span> theta, <span class="keywordtype">float</span> &amp;x, <span class="keywordtype">float</span> &amp;y, <span class="keywordtype">float</span> &amp;z)</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    {</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        x = rho * cosf(phi) * cosf(theta);</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        y = rho * sinf(phi);</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        z = rho * cosf(phi) * sinf(theta);</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    }</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        </div>
<div class="line"><a name="l00159"></a><span class="lineno"><a class="code" href="namespacegbmath.html#af60fd2cd2867f18928beb9f185e7c980">  159</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#af60fd2cd2867f18928beb9f185e7c980" title="Returns a gradual transition of &#39;x&#39; from 0 to 1 beginning at threshold &#39;a&#39; and ending at threshold &#39;b...">smoothstep</a>(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b, <span class="keywordtype">float</span> x)</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    {</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        <span class="keywordflow">if</span> (x &lt; a)</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        {</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            <span class="keywordflow">return</span> 0.0f;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;        }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (x &gt;= b)</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;        {</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            <span class="keywordflow">return</span> 1.0f;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        {</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;            x = (x - a) / (b - a);</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            <span class="keywordflow">return</span> x * x * (3.0f - 2.0f * x);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        }</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    }</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;</div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a4b9ccbf89172906f824d9c223a458ff9">  181</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespacegbmath.html#a4b9ccbf89172906f824d9c223a458ff9" title="Determines whether the two floating-point values f1 and f2 are close enough together that they can be...">closeEnough</a>(<span class="keywordtype">float</span> f1, <span class="keywordtype">float</span> f2)</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    {</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;        <span class="keywordflow">return</span> fabsf((f1 - f2) / ((f2 == 0.0f) ? 1.0f : f2)) &lt; <a class="code" href="namespacegbmath.html#acd96829ace89d35c295aac16fe50f3fc">EPSILON</a>;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    </div>
<div class="line"><a name="l00186"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a7b9af880500614372b44439d3d24aed9">  186</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespacegbmath.html#a7b9af880500614372b44439d3d24aed9">is_power2</a>(<span class="keywordtype">int</span> x)</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    {</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;        <span class="keywordflow">return</span> ((x &gt; 0) &amp;&amp; ((x &amp; (x - 1)) == 0));</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    }</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;</div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="code" href="namespacegbmath.html#aa1127e0ed6083818b38a89c063365c74">  192</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#aa1127e0ed6083818b38a89c063365c74" title="Clipping values ​​in a range between minimum and maximum inclusive. ">clump</a>(<span class="keywordtype">float</span> value, <span class="keywordtype">float</span> _min, <span class="keywordtype">float</span> _max)</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    {</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        <span class="keywordtype">float</span> r = value;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keywordflow">if</span>(r &lt; _min) r=_min;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <span class="keywordflow">if</span>(r &gt; _max) r=_max;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;        <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    }</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;</div>
<div class="line"><a name="l00201"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a1d44db3ba00e7255e2ddf760df556ffd">  201</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespacegbmath.html#a1d44db3ba00e7255e2ddf760df556ffd" title="sine and cosine. ">sincos</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> a, <span class="keywordtype">float</span>&amp; outSin, <span class="keywordtype">float</span>&amp; outCos) </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    {  </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;        outSin = sin(a); </div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;        outCos = cos(a); </div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    }</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="preprocessor">#if defined (_MSC_VER)</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#ifdef GBMATH_USE_ASM</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="preprocessor"></span><span class="keyword">inline</span> <span class="keywordtype">void</span> sincosAsm (<span class="keywordtype">float</span> a, <span class="keywordtype">float</span>&amp; s, <span class="keywordtype">float</span>&amp; c)</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;{</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    __asm  </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;            fld a;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            fsincos;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;            mov eax, [c];</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;            fstp [eax];</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;            mov eax, [s];</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;            fstp [eax];</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    };</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;};</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="preprocessor">#endif </span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00226"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ad7e5c294042e090b544f4c46e3694690">  226</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ad7e5c294042e090b544f4c46e3694690" title="Calculate the arc cotangent. ">arccot</a>(<span class="keywordtype">float</span> f) </div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;{</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;   <span class="keywordflow">return</span> atan(1.0f / f);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;</div>
<div class="line"><a name="l00232"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ae5ecfee596749b307ba5b1da2e4e703d">  232</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ae5ecfee596749b307ba5b1da2e4e703d" title="Calculate the arc tangent. ">arctg</a>(<span class="keywordtype">float</span> y, <span class="keywordtype">float</span> x)</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;{</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    <span class="keywordflow">return</span> atan2f(y, x);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;}</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;</div>
<div class="line"><a name="l00241"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a943dd559c743e425059e481a41d0e617">  241</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#a943dd559c743e425059e481a41d0e617" title="Same as acos(x), but if x is out of range, it is &quot;clamped&quot; to the nearest valid value. The value returned is in range 0...pi, the same as the standard C acos() function. ">safeAcos</a>(<span class="keywordtype">float</span> x)</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;{</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    <span class="comment">// Check limit conditions</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="keywordflow">if</span> (x &lt;= -1.0f)</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    {</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="namespacegbmath.html#a43466f850581872f732373ec59ea473b" title="PI. ">PI</a>; <span class="comment">//   constPi &lt;float&gt;(); // kPi;</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    }</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">if</span> (x &gt;= 1.0f)</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    {</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <span class="keywordflow">return</span> 0.0f;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;    }</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    <span class="comment">// Value is in the domain - use standard C function</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keywordflow">return</span> acos(x);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;}</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;</div>
<div class="line"><a name="l00259"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ad2ec5e3673fe6cd0408e75e2c9c0f170">  259</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ad2ec5e3673fe6cd0408e75e2c9c0f170" title="cotangent ">cotan</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> f) </div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;{  </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    <span class="keywordflow">return</span>   1.0f / tanf(f); </div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;}</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;</div>
<div class="line"><a name="l00265"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ad9e70f8fc15c2f3f164ed07448dd3b53">  265</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ad9e70f8fc15c2f3f164ed07448dd3b53" title="Angle in radians to degrees. ">radiansToDegree</a>(<span class="keywordtype">float</span> rad) </div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;{ </div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    <span class="keywordflow">return</span> rad * ( 180.0f /  <a class="code" href="namespacegbmath.html#a43466f850581872f732373ec59ea473b" title="PI. ">PI</a> ); </div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;}</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;</div>
<div class="line"><a name="l00272"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ab3b04e4d988b846e88d2b555bcca9540">  272</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ab3b04e4d988b846e88d2b555bcca9540" title="Angle in degrees to radians. ">degreeToRadians</a>(<span class="keywordtype">float</span> dgr)  </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;{ </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keywordflow">return</span> dgr * (  <a class="code" href="namespacegbmath.html#a43466f850581872f732373ec59ea473b" title="PI. ">PI</a> / 180.0f); </div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;}</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;</div>
<div class="line"><a name="l00278"></a><span class="lineno"><a class="code" href="namespacegbmath.html#afb3b41ebf2f06be87644ba1cfa8487c8">  278</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#afb3b41ebf2f06be87644ba1cfa8487c8" title="Normalization of the angle of rotation angle. Cast the value in the range -PI ... + PI ...">normalize_angle</a>( <span class="keywordtype">float</span> angle )</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;{</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keyword">static</span>  <span class="keyword">const</span> <span class="keywordtype">float</span> _PI_ = 3.1415926535898f;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    <span class="keyword">static</span>  <span class="keyword">const</span> <span class="keywordtype">float</span> TWO_PI = 6.2831853071795865f;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    <span class="keywordflow">return</span> (angle - TWO_PI *  floor( ( angle + _PI_ ) / TWO_PI) );</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;}</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;</div>
<div class="line"><a name="l00287"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a30eec791d5b4d5df94f6c11a991b8239">  287</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#a30742374d53e9b267e9efa8dc80a0a91" title="Calculate the linear interpolation. ">lerp</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> f1, <span class="keyword">const</span> <span class="keywordtype">float</span> f2, <span class="keyword">const</span> <span class="keywordtype">float</span> k) </div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;{ </div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    <span class="keywordflow">return</span> f1 + (f2 - f1) * k; </div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;}</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;</div>
<div class="line"><a name="l00293"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a2835c23a3b974829144107d2e021fbac">  293</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="namespacegbmath.html#a2835c23a3b974829144107d2e021fbac" title="rounding . ">round</a>(<span class="keywordtype">float</span> f) </div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;{  </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordflow">return</span> (<span class="keywordtype">int</span>)(f + (f &gt; 0 ? 0.5f : -0.5f));  </div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;}</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;<span class="preprocessor">#if defined (_MSC_VER)</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#ifdef GBMATH_USE_ASM</span></div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> roundAsm(<span class="keywordtype">float</span> a)</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;{</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    <span class="keyword">register</span> <span class="keywordtype">int</span> retval;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    __asm fld a</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    __asm fistp retval</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <span class="keywordflow">return</span> retval;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;}</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;</div>
<div class="line"><a name="l00315"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a92e2579b3533ef25c04dddb004adb4f2">  315</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span>   <a class="code" href="namespacegbmath.html#a92e2579b3533ef25c04dddb004adb4f2" title="Get an average of 3 values. ">max3</a> ( <span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b, <span class="keywordtype">float</span> c ) </div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;{ </div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <span class="keywordflow">return</span> a &gt; b ? (a &gt; c ? a : (b &gt; c ? b : c)) : (b &gt; c ? b : (a &gt; c ? a : c));  </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;}</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;</div>
<div class="line"><a name="l00323"></a><span class="lineno"><a class="code" href="namespacegbmath.html#aba8cda4d109bd7e51e5394a97118fdf0">  323</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#aba8cda4d109bd7e51e5394a97118fdf0" title="Compute and return the average (arithmetic) ">average_arithmetic</a>(<span class="keyword">const</span> <span class="keywordtype">float</span>* pf, <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> num)</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;{</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    <span class="keywordtype">float</span> r = 0.0f;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    <span class="keywordflow">if</span>(num==0) </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;        <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> c=0; c&lt;num; c++)</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    {</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;        r +=  *( pf + c );</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;    }</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordflow">return</span> r / (float)num;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;}</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;</div>
<div class="line"><a name="l00338"></a><span class="lineno"><a class="code" href="namespacegbmath.html#a65e7295323df3c440084df0638b1e2af">  338</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#a65e7295323df3c440084df0638b1e2af" title="Compute and return the geometric mean. ">average_geometric</a>(<span class="keyword">const</span> <span class="keywordtype">float</span>* pf, <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> num)</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;{</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <span class="keywordtype">float</span> r = 1.0f;</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <span class="keywordflow">if</span>(num==0) </div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> c=0; c&lt;num; c++)</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    {</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;        r *=  *( pf + c );</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;    }</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <span class="keywordflow">return</span>   pow( r, 1.0f/(<span class="keywordtype">float</span>)num );</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;}</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;<span class="keywordtype">float</span> <a class="code" href="namespacegbmath.html#ab6491049b7dbd6e1bdc31cb41c8660b5" title="random values ​​in the range ( 0.0f ... 1.0f ) ">random</a>();</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;</div>
<div class="line"><a name="l00356"></a><span class="lineno"><a class="code" href="namespacegbmath.html#ad7acbedef3d45b46710884c401ac51fd">  356</a></span>&#160;<span class="keyword">inline</span> BYTE <a class="code" href="namespacegbmath.html#ad7acbedef3d45b46710884c401ac51fd">scale_byte</a>( BYTE val, <span class="keywordtype">float</span> k )</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;{</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordtype">float</span> temp = (float)val;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    temp *= k;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    BYTE res = (BYTE) temp ;</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;}</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;</div>
<div class="line"><a name="l00364"></a><span class="lineno"><a class="code" href="namespacegbmath.html#aeb44b722761abeebc83964ceab6ce0f4">  364</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="namespacegbmath.html#aeb44b722761abeebc83964ceab6ce0f4">faster_floor</a>( <span class="keyword">const</span> <span class="keywordtype">float</span> x ) </div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;{ </div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <span class="keywordflow">return</span> x &gt; 0 ? (int)(x) : (int)(x) - 1; </div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;}</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="comment">//-------------------------------- asm  -----------------------------------</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160; </div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="preprocessor">#if defined (_MSC_VER)</span></div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#ifdef GBMATH_USE_ASM</span></div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> float_to_int_asm(<span class="keywordtype">float</span> f)</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;{</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    <span class="keywordtype">int</span> res;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    _asm</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    {</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;        fld f;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;        fistp res;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    };</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;}</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Sqrt_asm(<span class="keywordtype">float</span> Num)</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;{</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    _asm</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;        fld DWORD PTR [Num]</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;        fsqrt</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;        fstp DWORD ptr[Num]</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    };</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="keywordflow">return</span> Num;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;}</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Sin_asm( <span class="keywordtype">float</span> angle )</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;{</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    _asm</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    {</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;        fld  DWORD PTR [angle]</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        fsin</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;        fstp DWORD PTR [angle] </div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    };</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">return</span> angle;</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;}</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> Sincos_asm (<span class="keywordtype">float</span> a, <span class="keywordtype">float</span>&amp; s, <span class="keywordtype">float</span>&amp; c)</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;{</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    __asm  </div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    {</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        fld a;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        fsincos;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        mov eax, [c];</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;        fstp [eax];</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;        mov eax, [s];</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;        fstp [eax];</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    };</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;}</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Tan_asm(<span class="keywordtype">float</span> angle)</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;{</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    _asm</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    {</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;        fld DWORD  PTR [angle]</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;        fsincos</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;        fdiv</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;        fstp DWORD PTR [angle]</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    };</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordflow">return</span> angle;</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;}</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Atan_asm(<span class="keywordtype">float</span> angle)</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;{</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    _asm</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    {</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;        fld dword ptr  [angle]</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;        fld1</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;        fpatan</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;        fstp dword ptr [angle]</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    };</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <span class="keywordflow">return</span> angle;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;}</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Pow_asm(<span class="keywordtype">float</span> Base, <span class="keywordtype">float</span> Power)</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;{</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    _asm</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    {</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;        fld DWORD PTR [Power]</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;        fld DWORD PTR [Base]</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;        fld1</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;        fsub</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;        fyl2xp1</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;        sub     esp,16               ; z = x*log2 </div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;        fist    DWORD PTR [esp+12]   ; <a class="code" href="namespacegbmath.html#a2835c23a3b974829144107d2e021fbac" title="rounding . ">round</a> </div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;        fld1</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;        fstp    TBYTE PTR [esp]</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;        fisub   DWORD PTR [esp+12]   ; z - <a class="code" href="namespacegbmath.html#a2835c23a3b974829144107d2e021fbac" title="rounding . ">round</a> </div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;        mov     eax, [esp+12]</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;        add     [esp+8],eax</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;        f2xm1</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;        fld1</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;        fadd</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;        fld     TBYTE PTR [esp]    ; 2^(<a class="code" href="namespacegbmath.html#a2835c23a3b974829144107d2e021fbac" title="rounding . ">round</a> )</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;        fmul                       ; 2^z = e^x</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;        add     esp,16</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;        fstp DWORD PTR [Base]</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;    };</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keywordflow">return</span> Base;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;}</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;<span class="comment">// float cotan(const float f) {  return   1.0f / tanf(f); }</span></div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Cotan_asm(<span class="keyword">const</span> <span class="keywordtype">float</span> f) </div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;{  </div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    <span class="keywordflow">return</span> 1.0f / Tan_asm(f); </div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;}</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Asin_asm(<span class="keywordtype">float</span> angle)</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;{</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    angle = Sqrt_asm( angle*angle / (1.0f - angle*angle) );</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    <span class="comment">//Rad = Atan_asm(angle);</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    <span class="keywordflow">return</span> angle;</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;}</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">float</span> Acos_asm(<span class="keywordtype">float</span> angle)</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;{</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;    angle = Sqrt_asm((1.0f - angle*angle)/(angle*angle));</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;    <span class="comment">//angle = Atan_asm(angle);</span></div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    <span class="keywordflow">return</span> angle;</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;}</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;<span class="preprocessor">#endif </span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#endif </span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;}</div>
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&nbsp;&nbsp;&nbsp;<b>Project page:</b> &nbsp;<a target="_blank" href="https://code.google.com/p/gbmath/">https://code.google.com/p/gbmath/</a>&nbsp;&nbsp;<br>
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